What is multiexpfit ?

Multiexpfit includes programs for numerical data processing for
experimental sciences, for the evaluation
of physical processes characterized by exponential or
multi-exponential decays.

An experiment is performed as follows. A pump (for
example, a short laser pulse) excites some kind of
metastable states of a sample (for example, a fluorescent
dye). Then the sample decays, emitting the radiation, with
a multiexponential law. A time-resolved measure of the
emission F (decay) is done (for example, the intensity of
fluorescence). Also a time-resolved measure of the pump
is performed; we will call this the instrumental response
function (IRF).

The task that we want to perform is to express F
as the convolution of the IRF with the sum of a given number
of decaying exponentials, with time constant τn. The
quality of the fit will be evaluated as the mean square
difference between F and the convolutions.

The fit parameters are the τn and the amplitudes
An. Actually, also other parameters must be cosidered:
the time displacement δ between the measurement of
F and the IRF, and the background intensity of both F and
the IRF. The background intensity of the IRF is evaluated
from the starting part of the IRF, before the emission. The
background of F is the fit parameter b.

The program multiexp uses a generic non-linear fit algorithm
for finding the best fitting values for some of the parameters.
By default, only the τn are handled in this way. The values
of δ are discrete, so an exaustive scan of the values is
performed, inside a given range. The An and b values are
evaluated by an analytic formula, since the mean square error
is quadratic in both the An and b. It is possible to define
all these parameters in a way that they are handled by the generic
non-linear fit algorithm of minuit.

The IRF can be evaluated by measuring the decay of a short-living
exited state. In this case, a correction τR parameter can be
added, that represents the (short) decay time of the state. This
can be a fit parameter too, though it is preferred to use a known
value. (see M. Zuker et al, Delta function convolution method (DFCM)
for fluorescence decay experiments, Rev. Sci. Instrum. 56 (1) 1985)

The fit can be performed simulteneously on a set of F. In this case,
the parameters τn will be the same for all the F, and the
minimization of the mean square error will be performed. The set of F
will be divided into sub-sets, each one with a different IRF.

The program is based on minuit minimizer. A fcn
configuration file must
be provided (see section 3): it defines which file contains the
experimental data. After it has been called with
the configuration file name as argument, it opens a minuit session.
Operations are described in section 4.

A different way for processing the data is through moment evaluation (
see I. Isenberg, On the theory of fluorescence decay experiments,
J. Chem. Phys. 59 (10) 1973). In this case, the experimental data
are processed in order to evaluate the moments of the distributions. From the moments,
with no fit procedure, the decay times can be extracted by analytical procedures. This
is performed by moments program.